A student measures the mass of a metal block five times using a digital balance. His results are: 84.2 g, 84.3 g, 84.2 g, 84.3 g, 84.2 g. The manufacturer's specification states the true mass of the block is 86.5 g. Describe the accuracy and precision of these measurements and explain what type of error is most likely responsible for the difference between the mean of the student's results and the true value.

AQA A-Level Physics (7408) — 3.1.2 Limitations of Physical Measurements · Describe · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (5 marks)

The five readings are all 84.2 or 84.3 g, so the spread is only 0.1 g – the measurements are therefore precise.
The mean of the five readings is (84.2+84.3+84.2+84.3+84.2)/5 = 84.24 g, which is far from the true value of 86.5 g; the measurements are not accurate.
The difference between the mean (84.24 g) and the true value (86.5 g) is caused by a systematic error – the balance consistently gives readings that are too low, probably because it is not correctly zeroed or calibrated, so repeating the measurement does not reduce the error.

Examiner tips

  • Show the mean calculation to get the 84.24 g figure; this demonstrates accuracy assessment. Mention the small range (0.1 g) to justify precision. State that the error is systematic and explain it as a consistent bias such as zero‑error or mis‑calibration.

Common mistakes

  • Calculating the mean incorrectly or forgetting to include all five readings. Confusing precision with accuracy – e.g., saying the measurements are accurate because they are close together. Failing to identify the error as systematic rather than random.

Mark scheme (5 marks)

  1. The measurements are precise because the values are close together / there is a small range / low spread in the results
  2. The measurements are not accurate because the mean is not close to the true value (86.5 g)
  3. Correct calculation or identification of the mean as approximately 84.2 g or 84.24 g
  4. The type of error responsible is a systematic error
  5. Explanation of why it is systematic — the balance gives readings that are consistently too low / there is a zero error / the balance is not calibrated correctly, so repeating measurements does not reduce the error

Key terms in this question

accuracy · precision · mean · true value

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